[testplan-item] Chat input: allow to create new sessions easily

[benibenj]

Refs #284091

• anyOS @osortega
• anyOS @kycutler

Complexity: 3

Create Issue

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Context

A session type picker has been added near the chat input box in VS Code's chat view, allowing users to choose where their agent session will run. Users can select between local, background, or cloud sessions directly from the input area. The picker also supports changing the session type mid-conversation, enabling users to start in a local session and then continue in a background or cloud session.

Test Steps

1. Open the chat view in VS Code
2. Locate the session type picker near the chat input box at the bottom of the chat panel
3. Verify that the picker displays the available session types (local, background, cloud)
4. Select "local" session type and send a message
   • The session should run locally and respond appropriately
5. Select "background" session type and start a new session
   • The session should run in the background as expected
6. Select "cloud" session type and start a new session
   • The session should run in the cloud and respond appropriately
7. Start a local session, send a few messages, then change the picker to "background" or "cloud"
   • The session should seamlessly continue in the new session type
   • Previous context should be maintained
8. Verify the session type indicator reflects the current selection
9. Switch between multiple old sessions and make sure the picker updates correctly